886 MATHEMATICAL AND PHYSICAL SCIENCE. (Diss. VI. 
the railway system. The locomotive engine will ever rear. To M. de Pambour we are indebted? for by M. de Pam- 
remain as an invention entirely distinct from those far the best account of the elements of force contained wee on the 
created by the genius of Watt. It is in reality in- in the locomotive, and of the resistances which they foots 
dependent of his great principle of separate conden- have to overcome; but it is not to be doubted that tives. 
sation. It has a power of adaptation and a perfection much yet remains to be done in this direction. 
of performance more astonishing than any contrivance George Stephenson died 12th August 1848, atthe 407.) 
of our time, except perhaps the electric telegraph. age of sixty-eight, and generally respected for his Stephenson 
In 1552, Jerome Cardan took twenty-three days to private character as well as for his talents. His son saa 
travel from London to Edinburgh; that the same 
should be done 300 years later in eleven hours, and 
every day, is a fact as striking as any which the pro- 
gress of science presents. Whilst to Trevithick and 
George Stephenson we are mainly indebted for these 
results, the theory of the steam-engine is still in ar- 
had the honour of completing the second great railway 
work in Britain, from London to Birmingham, and 
by the invention of the tubular bridge, described in 
a previous section, he has added the most important, 
as well as the most scientific auxiliary to the exten- 
sion of railways since 1830. 
§ 6. Hydrodynamics, DUBUAT, VENTURI, Professor StToKES.—Friction and Resistance of Fluids. 
MM. Weser, Mr Scott RussELL.—Propagation of Waves. Influence on Canal Naviga- 
tion. MM. FourRNEYRON and PONCELET.—Improved Hydraulic Machines; Turbine. Reference 
to the subject of Capillary Attraction. 
(408.) There are few subjects less adapted for the kind 
Progress of of discussion which I have adopted in this Disserta- 
dor hi ~ tion than Hydrodynamics, whether in its abstract or 
practical form. Not only is it difficult to fix upon 
individuals who, in the more recent progress of the 
subject, have attached themselves to itin so especial 
a manner as to have impressed the science with the 
individual character of their own minds, but the pro- 
gress made in either branch has been of a remarkably 
fragmentary kind, usually bearing upon the solution of 
individual problems, and tending to the improvement 
of particular machines. Itmust be owned, too, that 
however important in practice may be the efficiency 
of a water-wheel or the discharge of a pipe, the so- 
lution of such problems does not present the attrac- 
tive interest which attaches to many less difficult ones 
in Natural Philosophy, As regards more general pro- 
blems of which a direct solution from first principles 
might appear possible, it has been found that these 
are as yet so limited as to give a character (which is 
generally admitted) of great barrenness to the theo- 
retical investigations, 
(409.) While, then, I shall endeavour, in conformity with 
my general plan, to preserve something of the bio- 
graphical character in the history, suppressing details 
and many minor and even some important steps, 
this section will necessarily have somewhat of a frag- 
mentary character, and its deficiencies must be sup- 
plied by a reference to the numerous articles of the 
Encyclopedia which treat more or less fully of these 
subjects and their history. 
(410.) 1, Friction and Resistance of Fluids.—The first 
Lee name I shall mention is that of the Chevalier Du- 
riction 
and resist- BUAT, Who has the signal merit of having attri- 
ance of buted due importance to, and of having considered 
fluids. 
with much sagacity, the effects of the friction of 
fluids against their own particles, and against the 
sides of the solid bodies used to confine them. He 
had the full advantage of an acquaintance with the 
Abbe Bossut’s excellent experiments and judicious 
writings, but he was, I believe, the first who suc- 
ceeded in ascribing to the diflerent forces which act 
on fluids in a state of uniform motion their effective 
share in determining their velocity. I refer particu- 
larly to the discharge of pipes and of rivers, Du- Theory of 
buat showed that when the motion of water in such ™Y*s 
circumstances becomes uniform, the accelerating force 
which acts is the measure of the total resistances to 
the fluid motion, whether arising from the inequali- 
ties of the bed or the viscosity of the fluid, These re- 
sistances are assumed to be proportional to the square 
of the velocity. Since they are exactly in proportion 
to the length of the pipe or channel, and since the 
moving pressure increases in the same proportion, the 
velocity is independent of the length of the pipe, whilst 
the inclination remains the same—a simple result not 
previously noticed. In the case of a pipe the head 
or superincumbent pressure may be divided into two 
parts; one, requisite to force the water into the tube 
with the requisite velocity, which is independent of 
the distance to be travelled; the other, which balances 
the resistance due to the length of the pipe, which 
for a given diameter varies as the length, or if the 
slope be constant is independent of the length. 
The relation of the area of the stream to the peri- 
meter or rubbing surface of the channel is then taken 
mean hydraulic depth. The manner in which Dubuat 
derives his formula (which I shall not here set down) 
from direct experiment, guided by a few general no- 
tions of theory, is a very good specimen of this kind 
1 The Theory of the Steam-Engine (1839), and A Practical Treatise on Locomotive Engines (1840), by the Comte F. M. G. de 
Pambour, 
Mean hy- 
* i! Ha ; draulic 
into account, This ratio is called by some writers the depth. 
